This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

Parameter estimation in nonlinear systems is an important issue in measurement, diagnosis and modeling. The goal is to find a differentiator free on-line adaptive estimation algorithm which can estimate the internal unknown parameters of dynamic systems using its inputs and outputs. This thesis provides new algorithms for adaptive estimation and control of nonlinearly parameterized (NLP) systems. First, a Hierarchical Min-max algorithm is invented to estimate unknown parameters in NLP systems. To relax the strong condition needed for the convergence in Hierarchical Min-max algorithm, a new Polynomial Adaptive Estimator (PAE) is invented and the Nonlinearly Persistent Excitation Condition for NLP systems, which is no more restrictive than LPE for linear systems, is established for the first time. To reduce computation complexity of PAE, a Hierarchical PAE is proposed. Its performance in the presence of noise is evaluated and is shown to lead to bounded errors. A dead-zone based adaptive filter is also proposed and is shown to accurately estimate the unknown parameters under some conditions. Based on the adaptive estimation algorithms above, a Continuous Polynomial Adaptive Controller (CPAC) is developed and is shown to control systems with nonlinearities that have piece-wise linear parameterizations. Since large classes of nonlinear systems can be approximated by piece-wise linear functions through local linearization...

In this Thesis, the development of the dynamic model of multirotor unmanned
aerial vehicle with vertical takeoff and landing characteristics, considering input
nonlinearities and a full state robust backstepping controller are presented. The
dynamic model is expressed using the Newton-Euler laws, aiming to obtain a better
mathematical representation of the mechanical system for system analysis and control
design, not only when it is hovering, but also when it is taking-off, or landing, or
flying to perform a task. The input nonlinearities are the deadzone and saturation,
where the gravitational effect and the inherent physical constrains of the rotors are
related and addressed. The experimental multirotor aerial vehicle is equipped with
an inertial measurement unit and a sonar sensor, which appropriately provides measurements
of attitude and altitude. A real-time attitude estimation scheme based on
the extended Kalman filter using quaternions was developed. Then, for robustness
analysis, sensors were modeled as the ideal value with addition of an unknown bias
and unknown white noise. The bounded robust attitude/altitude controller were derived
based on globally uniformly practically asymptotically stable for real systems,
that remains globally uniformly asymptotically stable if and only if their solutions
are globally uniformly bounded...

Fonte: The Institution of Engineering and TechnologyPublicador: The Institution of Engineering and Technology

Tipo: Artigo de Revista Científica

Publicado em //2013EN

Relevância na Pesquisa

15.8%

The problems of finite-time analysis and design for a class of Markov jump systems with Gaussian transition probabilities (TPs) are investigated in this study. Gaussian TP density function is introduced to quantise the stochastic uncertain information of TPs. Mode-dependent and variation-dependent controller is designed to make the resulting closed-loop systems finite-time bounded and finite-time stabilisable for all admissible unknown external disturbances and random uncertain TPs. It is shown that the approach proposed in the paper dealing with TPs outperforms available ones in literature to date, which is also confirmed by a numerical example.; Xiaoli Luan, Peng Shi and Fei Liu

This paper is devoted to design adaptive sliding-mode controllers for the Takagi-Sugeno (T--S) fuzzy system with mismatched uncertainties and exogenous disturbances. The uncertainties in state matrices are mismatched and norm-bounded, while the exogenous disturbances are assumed to be bounded with an unknown bound, which is estimated by a simple and effective adaptive approach. Both state- and static-output-feedback sliding-mode-control problems are considered. In terms of linear-matrix inequalities (LMIs), both sliding surfaces and sliding-mode controllers can be easily obtained via a convex optimization technique. Finally, two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper.; Jinhui Zhang, Peng Shi and Yuanqing Xia

We consider stationary consensus protocols for networks of dynamic agents
with switching topologies. The measure of the neighbors' state is affected by
Unknown But Bounded disturbances. Here the main contribution is the formulation
and solution of what we call the $\epsilon$-consensus problem, where the states
are required to converge in a tube of ray $\epsilon$ asymptotically or in
finite time.; Comment: 18 pages, 3 figures. The manuscript has been submitted for the
Special issue on Control and optimization in Cooperative Networks. Submitted
to SIAM SICON

We present a scalable set-valued safety-preserving controller for constrained
continuous-time linear time-invariant (LTI) systems subject to additive,
unknown but bounded disturbance or uncertainty. The approach relies upon a
conservative approximation of the discriminating kernel using robust maximal
reachable sets---an extension of our earlier work on computation of the
viability kernel for high-dimensional systems. Based on ellipsoidal techniques
for reachability, a piecewise ellipsoidal algorithm with polynomial complexity
is described that under-approximates the discriminating kernel under LTI
dynamics. This precomputed piecewise ellipsoidal set is then used online to
synthesize a permissive state-feedback safety-preserving controller. The
controller is modeled as a hybrid automaton and can be formulated such that
under certain conditions the resulting control signal is continuous across its
transitions. We show the performance of the controller on a twelve-dimensional
flight envelope protection problem for a quadrotor with actuation saturation
and unknown wind disturbances.

In communications, unknown variables are usually modelled as random
variables, and concepts such as independence, entropy and information are
defined in terms of the underlying probability distributions. In contrast,
control theory often treats uncertainties and disturbances as bounded unknowns
having no statistical structure. The area of networked control combines both
fields, raising the question of whether it is possible to construct meaningful
analogues of stochastic concepts such as independence, Markovness, entropy and
information without assuming a probability space. This paper introduces a
framework for doing so, leading to the construction of a maximin information
functional for nonstochastic variables. It is shown that the largest maximin
information rate through a memoryless, error-prone channel in this framework
coincides with the block-coding zero-error capacity of the channel. Maximin
information is then used to derive tight conditions for uniformly estimating
the state of a linear time-invariant system over such a channel, paralleling
recent results of Matveev and Savkin.

A robust controller is developed for uncertain, second-order nonlinear
systems subject to simultaneous unknown, time-varying state delays and known,
time-varying input delays in addition to additive, sufficiently smooth
disturbances. An integral term composed of previous control values facilitates
a delay-free open-loop error system and the development of the feedback control
structure. A stability analysis based on Lyapunov-Krasovskii (LK) functionals
guarantees uniformly ultimately bounded tracking under the assumption that the
delays are bounded and slowly varying.

This paper is concerned with a problem of robust filtering for a
finite-dimensional linear discrete time invariant system with two output
signals, one of which is directly observed while the other has to be estimated.
The system is assumed to be driven by a random disturbance produced from the
Gaussian white noise sequence by an unknown shaping filter. The worst-case
performance of an estimator is quantified by the maximum ratio of the
root-mean-square (RMS) value of the estimation error to that of the disturbance
over stationary Gaussian disturbances whose mean anisotropy is bounded from
above by a given parameter $a \ge 0$. The mean anisotropy is a combined entropy
theoretic measure of temporal colouredness and spatial "nonroundness" of a
signal. We construct an $a$-anisotropic estimator which minimizes the
worst-case error-to-noise RMS ratio. The estimator retains the general
structure of the Kalman filter, though with modified state-space matrices.
Computing the latter is reduced to solving a set of two coupled algebraic
Riccati equations and an equation involving the determinant of a matrix. In two
limiting cases, where $a = 0$ or $a \to +\infty$, the $a$-anisotropic estimator
leads to the standard steady-state Kalman filter or the $H_{\infty}$-optimal
estimator...

A procedure and theoretical results are presented for the problem of
determining a minimal robust positively invariant (RPI) set for a linear
discrete-time system subject to unknown, bounded disturbances. The procedure
computes, via the solving of a single LP, a polytopic RPI set that is minimal
with respect to the family of RPI sets generated from a finite number of
inequalities with pre-defined normal vectors.

In this paper, the tracking control problem of a class of uncertain
Euler-Lagrange systems subjected to unknown input delay and bounded
disturbances is addressed. To this front, a novel delay dependent control law,
referred as Adaptive Robust Outer Loop Control (AROLC) is proposed. Compared to
the conventional predictor based approaches, the proposed controller is capable
of negotiating any input delay, within a stipulated range, without knowing the
delay or its variation. The maximum allowable input delay is computed through
Razumikhin-type stability analysis. AROLC also provides robustness against the
disturbances due to input delay, parametric variations and unmodelled dynamics
through switching control law. The novel adaptive law allows the switching gain
to modify itself online in accordance with the tracking error without any
prerequisite of the uncertainties. The uncertain system, employing AROLC, is
shown to be Uniformly Ultimately Bounded (UUB). As a proof of concept,
experimentation is carried out on a nonholonomic wheeled mobile robot with
various time varying as well as fixed input delay, and better tracking accuracy
of the proposed controller is noted compared to predictor based methodology.

This paper considers the distributed consensus problem of linear multi-agent
systems subject to different matching uncertainties for both the cases without
and with a leader of bounded unknown control input. Due to the existence of
nonidentical uncertainties, the multi-agent systems discussed in this paper are
essentially heterogeneous. For the case where the communication graph is
undirected and connected, a distributed continuous static consensus protocol
based on the relative state information is first designed, under which the
consensus error is uniformly ultimately bounded and exponentially converges to
a small adjustable residual set. A fully distributed adaptive consensus
protocol is then designed, which, contrary to the static protocol, relies on
neither the eigenvalues of the Laplacian matrix nor the upper bounds of the
uncertainties. For the case where there exists a leader whose control input is
unknown and bounded, distributed static and adaptive consensus protocols are
proposed to ensure the boundedness of the consensus error. It is also shown
that the proposed protocols can be redesigned so as to ensure the boundedness
of the consensus error in the presence of bounded external disturbances which
do not satisfy the matching condition. A sufficient condition for the existence
of the proposed protocols is that each agent is stabilizable.; Comment: 16 page...

A resolved acceleration control (RAC) and proportional-integral active force
control (PIAFC) is proposed as an approach for the robust motion control of a
mobile manipulator (MM) comprising a differentially driven wheeled mobile
platform with a two-link planar arm mounted on top of the platform. The study
emphasizes on the integrated kinematic and dynamic control strategy in which
the RAC is used to manipulate the kinematic component while the PIAFC is
implemented to compensate the dynamic effects including the bounded
known/unknown disturbances and uncertainties. The effectivenss and robustness
of the proposed scheme are investigated through a rigorous simulation study and
later complemented with experimental results obtained through a number of
experiments performed on a fully developed working prototype in a laboratory
environment. A number of disturbances in the form of vibratory and impact
forces are deliberately introduced into the system to evaluate the system
performances. The investigation clearly demonstrates the extreme robustness
feature of the proposed control scheme compared to other systems considered in
the study.

A problem of vibration control of smart beams was addressed in various
publications which primarily utilize collocated sensors and actuators and
neglect the effect of measurement noise in the observer design. This paper
develops a natural design of an output controller which utilizes an
eigenfunction approximation of initial continuous model, eliminates control
spillover, and consequently leads to an efficient controller which marginalizes
effect of bounded system and measurement disturbances while reducing beam
vibrations. It is demonstrated that this control approach can be attained by a
non-collocated actuator and a point-sensor of velocity located nearly anywhere
on the beam. We show in simulations that the proposed methodology leads to an
efficient reduction of beam vibrations enforced by unknown bounded
disturbances.; Comment: 6 pages, 8 figures

The focus of this paper is on the co-design of control and communication
protocol for the control of multiple applications with unknown parameters using
a distributed embedded system. The co-design consists of an adaptive switching
controller and a hybrid communication architecture that switches between a
time-triggered and event-triggered protocol. It is shown that the overall
co-design leads to an overall switching adaptive system that has bounded
solutions and ensures tracking in the presence of a class of disturbances. In
order to achieve the goal of tracking persistent excitation techniques are
used.

This study develops an original and innovative matrix representation with
respect to the information flow for networked multi-agent system. To begin
with, the general concepts of the edge Laplacian of digraph are proposed with
its algebraic properties. Benefit from this novel graph-theoretic tool, we can
build a bridge between the consensus problem and the edge agreement problem; we
also show that the edge Laplacian sheds a new light on solving the leaderless
consensus problem. Based on the edge agreement framework, the technical
challenges caused by unknown but bounded disturbances and inherently nonlinear
dynamics can be well handled. In particular, we design an integrated procedure
for a new robust consensus protocol that is based on a blend of algebraic graph
theory and the newly developed cyclic-small-gain theorem. Besides, to highlight
the intricate relationship between the original graph and cyclic-small-gain
theorem, the concept of edge-interconnection graph is introduced for the first
time. Finally, simulation results are provided to verify the theoretical
analysis.; Comment: 22 pages, 10 figures; Submitted to International Journal of Robust
and Nonlinear Control

Normally, mini-aircraft must be able to perform tasks such as aerial photography, aerial surveillance, remote fire and pollution sensing, disaster areas, road traffic and security monitoring, among others, without stability problems in the presence of many bounded perturbations. The dynamical model is affected by blast perturbations. Based on this, it is possible to design, evaluate and compare the real result with respect to pitch control law based on reference trajectory in the presence of external disturbances (blasts) or changes in the aircraft controller model. The model has non-linear properties but, with soft perturbations through the aircraft trajectory, allows a linear description without losing its essential properties. The Laplace description is a transfer function that works to develop the state space, with unknown invariant parameters using a wind tunnel. Control law is based on a feedback sliding mode with decoupled disturbances, and the output result is compared with the real pitch position measured in the real system. The control law applied to the system has a high convergence performance.